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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Comparative study between experimental measurements and model predictions of bubble rise velocity in molten LiCl-KCl

This research investigated the shape and rise velocities of gas bubbles (helium, nitrogen, argon, and krypton) in molten LiCl-KCl at 500 °C using a specialized optical visualization apparatus. The apparatus features a custom quartz rectangular prism cell housed in a furnace, enabling the application of the shadowgraph measurement technique. Bubbles with diameters between 0.45 and 3.2 mm were produced via a capillary, and their equivalent diameters and rise velocities were analyzed using high-resolution imaging and centroid tracking algorithms. Important non-dimensional parameters were calculated to characterize behavior. Bubbles with 0.03 < Eo < 1.32, 17 < Re < 718, and Mo order of 10 -11 were generated in the molten LiCl-KCl, revealing that bubbles with diameters less than 1.46 mm remain spherical, whereas those with larger diameters are ellipsoidal. The transition and oscillation onset for bubble shape occurred at larger diameters than those previously observed in air–water systems. Comparative analysis of the gas-molten salt data against existing air–water bubble rise velocity correlations highlighted inaccuracies in predictions, particularly across the different bubble regimes. An existing correlation was calibrated to the molten salt data to improve the bubble velocity predictions. In conclusion, this study contributes essential experimental data for the design and safety evaluation of molten salt reactors and offers insights for the optimization of sparge systems for fission product removal.

Bubble rise velocity↗
DOE OSTI2024

Ion velocity effect governs damage annealing process in defective KTaO 3

Effects of electronic to nuclear energy losses (S e /S n ) ratio on damage evolution in defective KTaO 3 have been investigated by irradiating pre-damaged single crystal KTaO 3 with intermediate energy O ions (6 MeV, 8 MeV and 12 MeV) at 300 K. By exploring these processes in pre-damaged KTaO 3 containing a fractional disorder level of 0.35, the results demonstrate the occurrence of a precursory stage of damage production before the onset of damage annealing process in defective KTaO 3 that decreases with O ion energy. The observed ionization-induced annealing process by ion channeling analysis has been further mirrored by high resolution transmission electron microscopy analysis. In addition, the reduction of disorder level is accompanied by the broadening of the disorder profiles to greater depth with increasing ion fluence, and enhanced migration is observed with decreasing O ion energy. Since S e (~3.0 keV nm –1 ) is nearly constant for all 3 ion energies across the pre-damaged depth, the difference in behavior is due to the so-called 'velocity effect': the lower ion velocity below the Bragg peak yields a confined spread of the electron cascade and hence an increased energy deposition density. Here, the inelastic thermal spike calculation has further confirmed the existence of a velocity effect, not previously reported in KTaO 3 or very scarcely reported in other materials for which the existence of ionization-induced annealing has been reported. In other words, understanding of ionization-induced annealing has been advanced by pointing out that ion velocity effect governs the healing of pre-existing defects, which may have significant implication for the creation of new functionalities in KTaO 3 through atomic-level control of microstructural modifications, but may not be limited to KTaO 3 .

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Numerical modeling and experimental validation of low velocity impact of woven GFRP/CFRP composites

Low-velocity impact of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) composite laminates was studied experimentally and numerically. Hybrid laminates containing blocked layers of GFRP/CFRP/GFRP with all plies oriented at 0° were investigated. Relatively high impact energies were used to obtain full perforation of the laminate in a low-velocity impact setup. Numerical simulations were carried out using the in-house transient dynamics finite element code, Sierra/SM, developed at Sandia National Laboratories. A three-dimensional continuum damage model was used to describe the response of a woven composite ply. Two methods for handling delamination were considered and compared: (1) cohesive zone modeling and (2) continuum damage mechanics. The reduced model size achieved by omission of the cohesive zone elements produced acceptable results at reduced computational cost. Further, the comparison between different modeling techniques can be used to inform modeling decisions relevant to low velocity impact scenarios. The modeling was validated by comparing with the experimental results and showed good agreement in terms of predicted damage mechanisms and impactor velocity and force histories.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Comparison of interlaminar damage modeling strategies for hybrid composite/aluminum laminates subjected to low-velocity impact

Low-velocity impact of hybrid metal-composite structures was investigated experimentally and computationally. Composite laminates consisting of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) were joined with a 6061-T6 aluminum plate using an epoxy adhesive. Two variations of the structure were studied; one consisting of all plies oriented at 0° and one consisting of all plies oriented at 45°. A drop tower was used to impact structures at a range of energies, including energies above and below the threshold at which the aluminum layer was perforated. Numerical simulations were implemented using Sierra/SM, an in-house transient dynamics finite element code developed at Sandia National Laboratories. A Hosford plasticity model was used to describe the response of the aluminum layer. A newly implemented orthotropic continuum damage mechanics (CDM) constitutive model was used to represent the composite laminate. This 3D-CDM model was compared to a cohesive zone model (2D-CDM/CZM) to investigate efficacy of aluminum perforation energy prediction, delamination prediction, and computational cost. Accuracy of each model was evaluated using the experimental results. Each showed good agreement with the tests for both the force and velocity histories, as well as the observed damage mechanisms. The 2D-CDM/CZM model was marginally more accurate in capturing both the composite and aluminum behavior — this model averaged error percentages of -11.2% and 10.8% for residual velocity and peak force, respectively. Meanwhile, the 3D-CDM model predictions yielded average error percentages of -35.5% (velocity) and 22.6% (force). However, the 3D-CDM model generally resulted in a decreased computational cost; the average run time was 14% shorter than the 2D-CDM/CZM model and 3x as many timesteps per hour were computed using the same computational resources. In conclusion, new experimental data on the impact and perforation resistance of metal-composite laminates is presented in addition to numerical predictions of the impact behavior.

Carbon fiber↗
DOE OSTI2026

Conservative velocity mappings for discontinuous Galerkin kinetics

Continuum computational kinetic plasma models evolve the distribution function of a plasma species f s on a phase-space grid over time. In many problems of interest the distribution function has limited extent in velocity space; hence, using a uniform, highly refined mesh would be costly and slow. Nonuniform velocity grids can reduce the computational cost by placing more degrees of freedom where f s is appreciable and fewer where it is not. In this work we introduce a first-of-its kind discontinuous Galerkin approach to nonuniform velocity-space discretization using mapped velocity coordinates. This new method is presented in the context of a gyrokinetic model used to study magnetized plasmas. We create discretizations of collisionless and collisional terms using mappings in a way that exactly conserves particles and energy. Numerical tests of such properties are presented, and we show that this new discretization can reproduce earlier gyrokinetic simulations using grids with up to 6–60 times fewer cells and 22X-60X speed-ups depending on dimensionality, geometry and plasma parameters.

Discontinuous Galerkin↗
DOE OSTI2025

Multi-objective automatic discovery of optimized metamaterials for varying velocity impact protection

Mechanical metamaterials have demonstrated exceptional impact performance while remaining lightweight. Impact resistance has traditionally been investigated using quasi-static simulations, often with the assumption that performance will translate to high-velocity impact scenarios. However, critical crash protection parameters—such as peak stress and absorbed energy—are highly sensitive to impact velocity, leading to inconsistent performance under dynamic loading. To address this, we introduce a strain-rate-aware, active deep learning framework that enables multi-objective optimization of impact protection metrics across a wide range of impact velocities. Our framework captures the strain-rate sensitivity of architected lattices by learning to control spatial gradation in cellular metamaterials, resulting in over 200 % enhancement in impact protection relative to state-of-the-art designs such as Voronoi and re-entrant lattices. We demonstrate its practical utility by designing next-generation lattice structures for automotive bumper systems that satisfy multiple, velocity-specific safety criteria—capabilities beyond those of conventional designs. More than just a predictive tool, this framework marks the first step towards enabling adaptable impact-resistant structures across dynamic regimes.

Deep learning↗
DOE OSTI2024

Utilizing Quantum Cascade Lasers for Ultranarrow Velocity Resolution and Quantum-State Selectivity in Molecular Beam Scattering and Spectroscopy

Here, we demonstrate the capability of a narrow linewidth quantum cascade laser (QCL) to selectively excite a very narrow velocity range of nitric oxide (σ ≤ 7(3) m/s) with a pure ro-vibrational quantum state. By implementing a counter-propagating geometry, the molecules are selectively excited according to the Doppler shift of the ro-vibrational transition frequency such that the velocity width associated with the excited molecules depends only on the QCL linewidth. We demonstrate a velocity distribution limited by the effective linewidth of our free-running QCL (Γ = 3.2 MHz). Our development provides a cost-effective, flexible approach to resolve quantum-state selective chemical dynamics with excellent velocity resolution in a wide variety of molecules with infrared-active transitions. This technique has been formulated to provide ultrahigh collisional energy resolution in molecular beams to delineate final quantum-state product pairs in studies of molecular collisions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

ZTF SN Ia DR2 follow-up: Exploring the origin of the Type Ia supernova host galaxy step through Si II velocities

The relation between Type Ia supernovae (SNe Ia) and the stellar masses of their host galaxy is well documented. In particular, Hubble residuals display a distinct luminosity shift based on host mass. This is known as the mass step. This effect is widely used as an additional correction factor in the standardisation of SN Ia luminosities. We investigate the Hubble residuals and the mass step of normal SNe Ia in the context of Si IIλ6355 velocities based on 277 normal SNe Ia that are near their peak in the second data release (DR2) of the Zwicky Transient Facility (ZTF). We divided the sample into high-velocity (HV) and normal-velocity (NV) SNe Ia, separated at 12,000 km s −1 . This produced a sample of 70 HV and 207 NV objects. We then explored potential environment- and/or progenitor-related effects by investigating the Si IIλ6355 velocities with parameters such as the light-curve stretch x 1 , the colour c, and the host galaxy properties. Although we only find a marginal difference between the Hubble residuals of HV and NV SNe Ia, the NV mass step is 0.149 ± 0.024 mag (6.3σ). The HV mass step is smaller, 0.046 ± 0.041 mag (1.1σ), and is consistent with zero. The difference between the NV and HV mass steps is modest, at ∼2.2σ. Moreover, the clearest subtype difference appears for SNe in central regions (d DLR < 1), where NV SNe Ia show a large mass step, whereas HV SNe Ia are consistent with no step, yielding a difference of 3.1–3.6σ between NV and HV SNe Ia. We observe a host-colour step for both subtypes. NV SNe Ia show a step of 0.142 ± 0.024 mag (5.9σ), while HV SNe Ia show a step of 0.158 ± 0.042 mag (3.8σ), where the HV SNe Ia step appears to be larger, but the significance is lower because the sample size is smaller. Overall, the NV and HV colour steps are statistically consistent. HV SNe Ia also show modest (∼2.5–3σ) steps in certain subsets, such as those in outer regions (d DLR > 1), whereas NV SNe display stronger environmental trends. Our results indicate that NV SNe Ia appear to be more environmentally sensitive, particularly in central likely metal-rich and older regions, while HV SNe Ia show weaker and subset-dependent trends. This suggests that applying a universal mass-step correction might introduce biases, and that incorporating refined classifications and/or environment-dependent factors, such as the location within the host, might improve future cosmological analyses beyond the standard x 1 and c cuts.

supernovae: general↗
DOE OSTI2025

Velocity-space signatures of shock-drift acceleration at quasi-perpendicular collisionless shocks

The shock-drift acceleration of ions at quasi-perpendicular shocks is a well-known kinetic mechanism for the acceleration of a small fraction of incoming ions to high energy. Here, we use a suite of sixteen hybrid simulations of quasi-perpendicular collisionless shocks over the range of Alfvén Mach number 4.3 ≤ M A ≤ 15.8 (corresponding to a range of fast magnetosonic Mach numbers 2.6 ≤ M f ≤ 9.4) and shock-normal angle 45°≤ θ Bn ≤ 90° to identify the velocity-space signature of shock-drift acceleration using the field-particle correlation technique. We show that the features of the ion velocity distribution in the shock foot and ramp regions can be clearly interpreted by analysis of the single-particle trajectory of a reflected ion through the full 3D-3V phase space. The characteristic features of the velocity-space signature of shock-drift acceleration remain qualitatively robust over the full parameter range of our simulations, providing a potential means for its identification using single-point spacecraft measurements. At higher Alfvén Mach numbers M A ≳8 (M f ≳5), kinetic instabilities generate fluctuations of the electromagnetic fields within the shock transition region, leading to fluctuations in and smearing out of the resulting velocity-space signatures, but the signature remains generally robust and identifiable. The results on the shock-drift acceleration of ions presented here represent a novel means to determine more completely the partitioning of upstream bulk flow kinetic energy into plasma heating, particle acceleration, and electromagnetic fields in collisionless shocks.

Howes, Gregory G. [Univ. of Iowa, Iowa City, IA (U↗
DOE OSTI2024

Velocity profile shapes in Alcator C-Mod plasmas

Abstract Toroidal rotation velocity spatial profiles ( r / a < 0.8) have been obtained from C-Mod over a wide range of operational conditions, including H-mode, I-mode, ICRF-heated L-mode and Ohmic L-mode (LOC and SOC), and in plasmas with ITBs, LH wave injection and MCFD. Peaked, flat and hollow rotation profiles have been observed. In H- and I-mode plasmas, generally with co-current peaked profiles, the peaking is correlated with temperature profile peaking, and both increase with toroidal magnetic field (decrease with ρ ∗ ). Any dependence on density peaking is unclear. For Ohmic L-mode discharges, with LOC, the velocity profiles are usually flat and most often directed co-current, while with SOC the profiles are hollow, mostly co-current at the edge and counter-current in the core. Both of these Ohmic rotation states exist with matched density and temperature profiles (and gradients), indicating that neither gradient is relevant during rotation reversals. For plasmas with LH wave injection and discharges with ITBs, the velocity profiles are hollow while the density and temperature profiles exhibit substantial peaking. Broadly speaking for all operational regimes, there is no unifying ordering of the velocity gradient with plasma parameters.

Rice, J. E. (ORCID:0000000183195971)↗
DOE OSTI2024

Enhancement of magnetic domain wall velocity via resonant dissipation of standing wave modes of domain wall structure with perpendicular magnetic anisotropy

The dynamic behaviors of magnetic domain walls have significant implications for developing advanced spintronic devices. In this study, we investigate the intriguing resonance phenomenon within the magnetic domain wall structure, focusing on the dissipation mechanism and its impact on domain wall dynamic motion. By applying a static external magnetic field, we observe a remarkable amplification of domain wall velocity through the resonant excitations of the flexure modes. The resonance of the flexure mode exerts an indirect influence on the domain wall velocity through energy dissipation, leading to a significant enhancement from the predictions of the one-dimensional Walker model. We establish a robust model platform rooted in energy dissipation allows comprehensive understanding the dramatic enhancement of domain wall velocity observed during width-directional flexure mode resonance. By directly quantifying energy dissipation, our approach provides highly effective and accurate estimates of domain wall velocity, surpassing previous methods that focus solely on the instantaneous dynamics of the domain wall structure. These findings offer crucial insights into the fundamental mechanisms governing the dynamics of domain walls and other magnetic systems, such as magnetic skyrmions, bubbles, and magnetic vortices, paving the way for development and optimization of next-generation spintronic devices.

Collective dynamics↗
DOE OSTI2025

Mapping Spatiotemporal Solvent Velocity from Measured Concentration Gradients in a Polarized Electrolyte

The electric-field induced motion of neutral species impedes the efficacy of electrochemical devices. By combining operando X-ray transmission measurements with continuum mechanics, we have developed a methodology for determining the velocity of neutral solvent molecules under an applied field. The X-ray transmission experiments were used to determine ion concentration profiles as a function of space and time in a polymer electrolyte. The unsteady state solvent mass balance equation was solved numerically with experimental concentration profiles to map spatiotemporal solvent velocities. We compare our experimentally derived results with predictions made with concentrated solution theory. We use the cation transference number as the only adjustable parameter to match experimental measurements of both concentration and solvent velocity. Our approach may be used to determine solvent velocity with any operando technique used to measure time-dependent ion concentration profiles.

Abdo, Emily E↗
DOE OSTI2025

Investigation of Site Amplifications Using Ambient-Noise-Derived Shallow Velocity Structures Under a Dense Array in Oklahoma

The shear-wave velocity (V S ) structure plays an important role in characterizing site amplification. The Large-n Seismic Survey in Oklahoma (LASSO; 1820 stations) revealed large vertical ground-motion variability in a 25 km × 32 km area in northern Oklahoma. The LASSO array has a relatively simple and flat topography, typical in a sedimentary basin environment in the central United States. In this study, we use the dense array to investigate the velocity structure under the LASSO array and how vertical ground motions relate to the shallow-to-deep structures. We extract the fundamental-mode Rayleigh wave by cross-correlating one month of ambient noise (0.7–5 Hz). We use double-beamforming to measure the group and phase velocities and anisotropy. By jointly inverting the group and phase velocities, we obtain the V S structure. Here, we observe correlations between V S at depths of 0.1–1.5 km and vertical ground motions using sites on the stiffer Permian formations. The shallow Quaternary alluvium and terrace deposits can amplify vertical ground motions by a factor of 2–4.5 between 2 and 25 Hz and attenuate signals above 25 Hz. We use 1D V S profiles to simulate the SV-wave transfer functions. An average V S of 250 m/s in the upper 20–40 m may cause the observed amplification between 2 and 40 Hz. V S estimated by topographic slopes cannot predict the relative amplification. Our results highlight the large variability of site-dependent ground motion in a small local region and the importance of characterizing shallow structures to estimate seismic hazards. Small thickness variations of the shallow formation can significantly change the resonance amplitude and frequency, which likely reduces the coherency of the Rayleigh waves extracted from ambient noise.

Chang, Hilary [Massachusetts Inst. of Technology (↗
DOE OSTI2024

Hypersonic Wake Velocity Measurements Using Acetone Molecular Tagging Velocimetry

A non-intrusive laser diagnostic known as molecular tagging velocimetry was used to find quantitative off-body velocity measurements in the wake of a sphere in the Mach 7 Ludwieg Tube Wind Tunnel located at The University of Texas at San Antonio. Acetone gas seeded in the flow was excited using the 4th harmonic of a pulse-burst Nd:YAG laser. The experimental results were used to validate and compare to simulations using a continuous Galerkin flow solver. Both the experimental and simulated results agreed on negative velocities in the viscous shear layer. Near the centerline of the sphere, average velocities of -200 m/s were observed due to reverse flow in the recirculation region. Outside of the shear layer, velocities of 800 m/s were observed in both the experimental and simulated results. The overall average uncertainty for the strut-mounted and free-flight case was estimated to be ±27 m/s. The flow features of the wake were visualized using schlieren imaging, and the experimental results agreed well with the simulated results.

Shoemake, Lawton↗
DOE OSTI2026

Characterizing the Velocity Anisotropy of the Milky Way’s Stellar Halo

Abstract Modeling the Milky Way stellar halo requires well-determined density and velocity anisotropy profiles. However, it has been challenging to gather a large sample of stars with six-dimensional data that extend beyond 40 kpc to map the outer halo. Our work investigates the velocity anisotropy in the Milky Way stellar halo with more than 10,000 blue horizontal-branch stars, combining Gaia astrometric data and spectroscopic data from SEGUE, DESI, and LAMOST. This large sample allows us to obtain a detailed profile of up to ∼50 kpc. Radial velocities are predominant in the inner halo (<30 kpc), and the anisotropy presents a smooth decrease before rapidly dropping to negative values, becoming dominated by tangential dispersion velocities. Removing the main known accreted structures of the Milky Way makes the anisotropy profile radially dominated at all radii. Our profile clearly shows an increase in the anisotropy from the center of the Galaxy, in accordance to the simulations. We also investigate the correlation of anisotropy with metallicity and with color. The lack of correlation between metallicity and anisotropy in our clean sample reinforces that this relation is driven by merger events. The initial exploration with color indicates a relation between kinematics and age, showing that older stars are dynamically colder and present less radial orbits than younger stars in the inner halo.

Barbosa, F. O. [Universidade de São Paulo] (ORCID:↗
DOE OSTI2026

Towards retrieving cloud top entrainment velocities from MISR cloud motion vectors

Although important, direct retrievals of entrainment rates in cloud-topped planetary boundary layer (PBL) remain elusive. Here we present a novel technique for retrieving cloud-top entrainment velocities using only Multi-angle Imaging Spectro-Radiometer (MISR) stereoscopic retrievals of cloud-motion vectors (CMVs) and cloud-top heights (CTHs). Mesoscale vertical air velocity at CTH is diagnosed from the continuity equation and then used to derive entrainment velocities from the PBL mass-budget equation. The algorithm is demonstrated through a case of marine stratocumulus deck off the California coast, with comparisons made against data from the European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis (ERA5) and the data from other satellites. MISR low-cloud CTH for this case were lower than the ERA5 reported PBL depth by 189 ± 87 m. These differences in cloud top heights partly modulate the differences in the ERA5 and MISR horizontal winds, with larger differences in meridional over zonal wind components. Average difference between ERA5 and MISR derived mesoscale vertical air motion at cloud top was 0.14 ± 0.73 cm s −1 , while the same for entrainment rate was −0.09 ± 0.46 cm s −1 . The uncertainties in the utilized CTHs and CMVs are propagated to derive systematic and random retrieval uncertainties. Fractional uncertainty is lower than 25 % when the retrieved mesoscale vertical air motion is stronger than ±0.04 cm s −1 and entrainment velocities are stronger than ±0.03 cm s −1 . These results showcase the ability to derive mesoscale vertical air motion and entrainment rates from MISR observations and motivate its extension to generate a global climatology leveraging its full 23-year record (2000–2022). Nonetheless comprehensive validation of the retrievals is warranted through comparisons with estimates from an independent dataset across diverse weather conditions.

Mitra, Arka [Argonne National Laboratory (ANL), Ar↗
DOE OSTI2025

The DESI DR1 Peculiar Velocity Survey: Mock Catalog

We describe the production of the official set of mock catalogs for the Dark Energy Spectroscopic Instrument Peculiar Velocity Survey (DESI-PV) Data Release 1 (DR1). Our mock catalogs reproduce the Bright Galaxy Survey number density and clustering at low redshift $(z<0.1)$ and the DESI PV samples of Fundamental plane and Tully-Fisher distances, from which we derive peculiar velocities. We carefully match mock and data properties and we mimic measurements of distance indicators and peculiar velocities, which follow the same statistical properties as real data. Mock samples of type-Ia supernovae also complement the other two distance indicators. Our 675 available mock realizations were used consistently by our three different methodologies described in our companion papers that measure the growth rate of structure $fσ_8$ with DESI PV DR1. Those mocks allow us to perform precise tests of clustering models and uncertainty estimation to an unprecedented level of accuracy, and compute correlations between methodologies. The consensus value for the DESI DR1 PV growth rate measurement is $fσ_8 = 0.450 \pm 0.055$. This sample of mock catalogs represents the largest and most realistic set for cosmological measurements with peculiar velocities to date.

Bautista, J. [Marseille, CPPM]↗
DOE OSTI2024

Sound Velocities of Stishovite at Simultaneous High Pressure and High Temperature Suggest an Eclogite‐Rich Layer Beneath the Hawaii Hotspot

Compressional and shear wave velocities of polycrystalline stishovite (SiO 2 ) have been measured at simultaneous high pressures and temperatures up to 14.5 GPa and 800°C. By fitting velocities to the finite strain equations, the elastic moduli and density were determined to be K S0 = 306.6(46) GPa, $K$$^{′}_{S}$ = 4.92(10), ∂K S /∂T = −0.024(1) GPa/K, G 0 = 229.0(34) GPa, G′ = 1.07(10), ∂G/∂T = −0.017(1) GPa/K, ρ 0 = 4.287(2) g/cm 3 . Our modeling suggested that, in the eclogite, coesite-stishovite transition can increase P and S wave velocities by 2.4% and 3.5%, respectively. A comparison between geophysical observations and our model shows that the coesite-stishovite phase transition in the eclogite can potentially be responsible for the occurrence of the X discontinuity beneath Hawaii. In addition, our current results suggest an eclogite-rich layer between 340 and 450 km depth beneath Hawaii. The eclogite concentration at the top and bottom of the layer is 41–55 vol% and >77 vol%, respectively.

36 MATERIALS SCIENCE↗